To study the spatial distribution and scale of oil and gas near faults in petroliferous basins, a prediction model is established for the degree of damage that faults in different stages of evolution exert on the sealing ability of mudstone cap rocks by calculating the stages and degree of fault damage to the sealing ability of mudstone cap rocks. This model is applied to the Nanpu 5th Structure and the results show that at survey lines L2 and L8, the F1 Fault destroyed the sealing capacity of mudstone cap rock of the 2nd member of Dongying Formation (E3d2). The undamaged cap rock stage, when the degree of damage was zero, persisted from 23.8 to 16.0 Ma at survey line L2 and from 23.8 to 13.6 Ma at survey line L8. Complete destruction, i.e., where the degree of damage was 100%, at survey lines L2 and L8 occurred from 16.0 to 13.3 Ma and from 13.6 to 13.3 Ma, respectively. The partial destruction stage began 13.3 Ma ago and persists today; the degrees of damage at survey lines L2 and L8 were 89.96% and 82.58%, respectively. This was not conducive to oil and gas accumulation in the reservoir under the mudstone cap rock of E3d2. These results agreed with the current findings of small amounts of oil and gas under the mudstone cap rock of E3d2 at survey line L8 and no oil and gas at survey line L2. This indicates that the model is feasible for predicting the degree of damage to the sealing ability of the mudstone cap rocks by faults at different stages in their evolution.